JP2014086599A - Optical fiber - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an excitation mode of basic mode, and to ensure that the gain of signal light in higher-order mode is equal to or higher than the gain in basic mode.SOLUTION: In an optical fiber having a step refractive type index distribution mainly composed of silica glass and having a core and a cladding, when a concentration of a rare earth element in a range of radius a3 from the center of core is denoted by d1, and the concentration of a rare earth element in a range of radius a2 from the radius a3 of the core is denoted by d2, it is ensured that the gain in the higher-order mode of signal light propagating through the optical fiber is equal to or higher than the gain in the basic mode by selecting the value of d1/d2 suitable for the value of a2/a1.

Description

  The present invention relates to an amplifying optical fiber for realizing a long distance in multimode transmission using a plurality of modes.

  In recent years, Internet traffic has continued to increase due to the diversification of services, and the transmission capacity has increased dramatically due to the increase in the number of wavelength multiplexing by the increase in the transmission speed and the wavelength division multiplexing (WDM) technology. . Further, in recent years, further expansion of transmission capacity is expected by digital coherent technology which has been actively studied. In digital coherent transmission systems, frequency utilization efficiency has been improved by using multilevel phase modulation signals, but higher signal-to-noise ratios are required. However, in a transmission system using a conventional single mode fiber (SMF), the transmission capacity is expected to saturate at 100 Tbit / sec due to input power limitation due to nonlinear effects in addition to the theoretical limit. Therefore, further increase in capacity has become difficult.

  In order to further increase the transmission capacity in the future, a medium that realizes innovative transmission capacity expansion is required. Therefore, mode multiplex transmission using a multimode fiber (MMF) that can be expected to improve the signal-to-noise ratio and the space utilization efficiency by using a plurality of propagation modes in an optical fiber as a channel is attracting attention. . Up to now, high-order modes propagating in the fiber have been a cause of signal degradation. However, active use is being studied in the development of digital signal processing, multiplexing / demultiplexing techniques, etc. 2).

  The expansion of transmission capacity using MMF has been remarkable in recent years, and has reached 26.4 Tbps in the DP-QPSK system using a three-mode fiber (see, for example, Non-Patent Document 3).

In addition, studies have been made to increase the distance of multimode transmission, and reports have been made on the amplification of the LP01 mode as a basic mode and the LP11 mode as a first higher-order mode using an Er ³⁺ doped optical amplifier. (For example, refer nonpatent literature 4.).

  In order to maintain the transmission quality of all modes in order to increase the distance of multimode transmission, it is essential to adjust the gain of each mode in the optical amplifier. The gain of each mode is determined by the overlap between the excitation element number distribution determined by the electric field distribution of the excitation light incident on the amplification optical fiber and the rare earth element addition distribution and the electric field distribution of the signal light. At present, there are two main structures of the rare earth element added region of the amplification fiber: a step index type structure in which a rare earth element is added to the entire core and a center dope type structure in which a rare earth element is added only at the center of the core.

  However, in an amplification optical fiber that requires a gain comparable to that of the fundamental mode in a higher-order mode, a structure in which a rare earth addition distribution is heavily doped at the edge of the fiber core as in Non-Patent Document 4 has been proposed. In Non-Patent Document 4, the excitation conditions are adjusted to adjust the gains of the LP11 and LP01 modes.

N. Hanzawa et al. , “Demonstration of Mode-Division multiplexing Transmission 10 km Two-mode Fiber with Mode Coupler” OFC2011, paper OWA4 T.A. Sakamoto et al. , “Modal Disposition Compensation Technology for Long-haul Transmission over Few-mode Fiber with SIMO Configuration”, ECOC2011, We. 10. P1.82 2E. Ipetal, “88 × 3 × 112-Gb / s WDM Transmission over 50 km of Three-Mode Fiber with Inline Few-Mode Fiber Amplifier” EcoC2011, paper Thr. 13. C. 2 Y. Jung et al. , “Detailed study of modal gain in a multimode EDFA supporting LP01 and LP11 mode group amplification” OFC / NFOEC 2012 paper OM3C4

  However, the gain of the LP01 mode is 4-5 dB larger than the gain of the LP11 mode, and when long-distance transmission is performed, the gain of the higher-order mode signal cannot be obtained compared to the basic mode and the quality is deteriorated. was there. In general, higher order modes have higher transmission loss and bending loss than the fundamental mode, so it is desirable to obtain a gain higher than the fundamental mode.

  An object of the present invention is to set the excitation mode to the fundamental mode and to make the gain of the signal light in the higher-order mode equal to or higher than the gain of the fundamental mode.

  The optical fiber of the present invention is an optical fiber having a step-type refractive index profile mainly composed of silica glass having a core and a cladding, wherein the concentration of the rare earth element in the range of radius a3 from the center of the core is d1, When the concentration of the rare earth element in the range from the radius a3 to the radius a2 is d2, the gain in the higher order mode of the signal light propagating through the optical fiber is selected by selecting a value of d1 / d2 suitable for the value of a2 / a1. The gain is higher than the basic mode.

  Specifically, the optical fiber of the present invention is an optical fiber mainly composed of silica glass having a core and a cladding having a refractive index lower than that of the core around the core and having a step-type refractive index distribution. A first region of the core located within a radius a3 from the center of the core and having a rare earth element concentration d1; and a radius of the core of the core a3 to a2 And a second region in which the concentration of the rare earth element is d2, and a2 = a1, 0.5 ≦ a3 / a1 <0.6, and d1 / d2 ≦ 0.375, Alternatively, a2 = a1 and 0.6 ≦ a3 / a1 <0.8 and d1 / d2 ≦ 0.44 or a2 = a1 and 0.8 ≦ a3 / a1 <0 .9 and d1 / d2 ≦ 0.375, or a = Is a1, a 0.9 ≦ a3 / a1 <1, characterized in that it is a d1 / d2 ≦ 0.16.

  Specifically, the optical fiber of the present invention is an optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile, and has a radius from the center of the core of the core. a first region disposed in the range of a3 and having a rare earth element concentration of d1, and a second region of the core disposed in a range of the core from a radius to a2 and having a rare earth element concentration of d2. 0 ≦ d1 / d2 ≦ 1/10, 0.65 ≦ a2 / a1 <0.7, and 0.25 ≦ (a2-a3) /a1≦0.48 Or 0 ≦ d1 / d2 ≦ 1/10, 0.7 ≦ a2 / a1 <0.8, and 0.14 ≦ (a2-a3) /a1≦0.48, or 0 ≦ d1 / d2 ≦ 1/10, 0.8 ≦ a2 / a1 <0.9, 0 023 ≦ (a2−a3) /a1≦0.48, or 0 ≦ d1 / d2 ≦ 1/10, 0.9 ≦ a2 / a1 <1.0, and 0.0 ≦ ( a2-a3) /a1≦0.48.

  Specifically, the optical fiber of the present invention is an optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile, and has a radius from the center of the core of the core. a first region disposed in the range of a3 and having a rare earth element concentration of d1, and a second region of the core disposed in a range of the core from a radius to a2 and having a rare earth element concentration of d2. 1/10 <d1 / d2 ≦ 1/8, 0.6 ≦ a2 / a1 <0.7, and 0.36 ≦ (a2−a3) /a1≦0.47 Or 1/10 <d1 / d2 ≦ 1/8, 0.7 ≦ a2 / a1 <0.8, and 0.15 ≦ (a2-a3) /a1≦0.49. Or 1/10 <d1 / d2 ≦ 1/8 and 0.8 ≦ a2 / a1 <0.9 Yes, 0.06 ≦ (a2−a3) /a1≦0.49, or 1/10 <d1 / d2 ≦ 1/8, 0.9 ≦ a2 / a1 <1.0 0.01 ≦ (a2−a3) /a1≦0.49.

  Specifically, the optical fiber of the present invention is an optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile, and has a radius from the center of the core of the core. a first region disposed in the range of a3 and having a rare earth element concentration of d1, and a second region of the core disposed in a range of the core from a radius to a2 and having a rare earth element concentration of d2. 1/8 <d1 / d2 ≦ 1/6, 0.65 ≦ a2 / a1 <0.7, and 0.3 ≦ (a2−a3) /a1≦0.47 Or 1/8 <d1 / d2 ≦ 1/6, 0.7 ≦ a2 / a1 <0.8, and 0.24 ≦ (a2−a3) /a1≦0.47. Or 1/8 <d1 / d2 ≦ 1/6 and 0.8 ≦ a2 / a1 <1.0 Characterized in that it is a 0.17 ≦ (a2-a3) /a1≦0.47.

  Specifically, the optical fiber of the present invention is an optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile, and has a radius from the center of the core of the core. a first region disposed in the range of a3 and having a rare earth element concentration of d1, and a second region of the core disposed in a range of the core from a radius to a2 and having a rare earth element concentration of d2. 1/6 <d1 / d2 ≦ 1/4, 0.7 ≦ a2 / a1 <0.8, and 0.36 ≦ (a2−a3) /a1≦0.43 Or 1/6 <d1 / d2 ≦ 1/4, 0.8 ≦ a2 / a1 <0.9, and 0.27 ≦ (a2−a3) /a1≦0.43. Or 1/6 <d1 / d2 ≦ 1/4, 0.9 ≦ a2 / a1 <1.0 Characterized in that it is a 0.35 ≦ (a2-a3) /a1≦0.43.

  In the optical fiber of the present invention, the rare earth element may include erbium.

  In the optical fiber of the present invention, the core may be added with aluminum or germanium in addition to the rare earth element.

  The above inventions can be combined as much as possible.

  According to the present invention, the excitation mode is the fundamental mode, and the gain of the signal light in the higher order mode can be made higher than the gain of the fundamental mode. This makes it possible to maintain stable transmission quality in each mode when information is transmitted in a plurality of modes.

An example of the refractive index distribution of the optical fiber for amplification is shown. An example of the region of the core radius a and the relative refractive index difference Δ for satisfying a desired bending loss when the propagation mode is the LP01 mode and the LP11 mode is shown. An example of the rare earth addition distribution of the optical fiber which concerns on this embodiment is shown. Gain difference between LP11 mode and LP01 mode when a3 / a1 is changed from 1/7 to 6/7 and d1 / d2 is changed from 1 to 1/10 at a1 = 7 μm, a1 = a2, and d1 = 50 ppm. An example of the simulation result is shown. Gain difference between LP11 mode and LP01 mode when a3 / a1 is changed from 1/7 to 6/7 and d1 / d2 is changed from 1 to 1/10 at a1 = 4 μm, a1 = a2, and d1 = 50 ppm. An example of the simulation result is shown. Gain difference between LP11 mode and LP01 mode when a3 / a1 is changed from 1/7 to 6/7 and d1 / d2 is changed from 1 to 1/10 at a1 = 6 μm, a1 = a2, and d1 = 50 ppm. An example of the simulation result is shown. An example of a gain difference between the LP11 mode and the LP01 mode when a2 / a1 and (a2-a3) / a1 are variables when d1 / d2 = 1/10 is shown. An example of the gain difference between the LP11 mode and the LP01 mode when a2 / a1 and (a2-a3) / a1 are variables at d1 / d2 = 1/8 is shown. An example of the gain difference between the LP11 mode and the LP01 mode when a2 / a1 and (a2-a3) / a1 are variables at d1 / d2 = 1/6 is shown. An example of the gain difference between the LP11 mode and the LP01 mode when a2 / a1 and (a2-a3) / a1 are variables at d1 / d2 = 1/4 is shown. An example of the gain difference between the LP11 mode and the LP01 mode when a2 / a1 and (a2-a3) / a1 are variables at d1 / d2 = 1/2 is shown.

  Embodiments of the present invention will be described with reference to the accompanying drawings. The embodiments described below are examples of the present invention, and the present invention is not limited to the following embodiments. In the present specification and drawings, the same reference numerals denote the same components.

  After explaining the basic theory of amplification for gain equalization in each mode, a simulation based on the theory is performed, and the best mode of the rare earth addition distribution of the amplification optical fiber is shown. Here, the rare earth element to be added is erbium (Er) and will be described below.

ここでＰ_ｓ，ｉはｉモード目の信号光および自然放出光のパワー、ｚはＥＤＦにおける光の伝搬方向、νは光の波長である。ｉモード目の信号光利得係数γ_ｅ，ｉ（ｚ，ν）と吸収係数γ_ａ，ｉ（ｚ，ν）は各モードの規格化電界分布ψ_ｓ，ｉ（ν，γ，θ）と信号光、励起光に対する放出断面積σ_ｅｓ，ｉ ^ｓ、吸収断面積σ_ａｓ，ｉ ^ｓを用いてそれぞれ以下のように表せる。

Ｎ_２（γ，θ，Ｚ）とＮ_１（γ，θ，Ｚ）は、それぞれ位置ｚにおけるファイバ断面の１点を動径ｒと偏角をθで表したときの、Ｅｒ^３＋励起準位と基底準位のイオン数を表す。各伝搬モードにおいて数式１の伝搬方程式を解くことによりモード間の利得差を小さくする構造が特定される。 When the rate equation when Er is considered as a three-level system is solved and the propagation equation of EDF (Erbium-doped fiber) is obtained, it can be expressed as the following Equation 1.

Here, P _{s, i} is the power of the i-mode signal light and spontaneous emission light, z is the light propagation direction in the EDF, and ν is the wavelength of the light. The i-mode signal light gain coefficient γ _{e, i} (z, ν) and the absorption coefficient γ _{a, i} (z, ν) are the normalized electric field distribution ψ _{s, i} (ν, γ, θ) and signal of each mode. light, expressed as follows using the respective emission cross section sigma _es, ^{i s,} the absorption cross section sigma _{the as,} ^{i s} to the excitation light.

N ₂ (γ, θ, Z) and N ₁ (γ, θ, Z) are Er ³⁺ excitation levels when one point of the fiber cross section at the position z is represented by a radius r and a declination θ, respectively. And the number of ions in the ground level. By solving the propagation equation of Equation 1 in each propagation mode, a structure for reducing the gain difference between the modes is specified.

  As the excitation light source for the Er-doped amplification fiber (EDF), the 980 nm band and the 1480 nm band are generally used. In this simulation, the mode does not change greatly due to the difference in the light source, and the same tendency is observed. In this simulation, a light source of 1480 nm is used, the input power is 100 mW, and the length of the EDF is 15 m. The signal light is 1550 nm and the input power is -17 dBm.

  In mode multiplexing transmission, all modes are required to realize a desired bending loss. ITU-T G. The recommended bending loss at 652 is 0.5 dB / 100 turn or less at a bending radius of 30 mm. FIG. 1 shows the refractive index distribution of the amplification optical fiber used in this simulation.

  This structure is assumed to have a core diameter of a1, a step type with a relative refractive index difference between the core and the clad of Δ, a used wavelength of 1530 to 1565 nm in the C band, a bending loss of 0.1 dB / 100 turn or less, and a propagation mode of FIG. 2 shows the calculated design range for the LP01 mode and the LP11 mode.

ｎ_ｃｏｒｅおよびｎ_ｃｌａｄはそれぞれコアおよびクラッドの屈折率である。ａ１＝７μｍ、Δ＝０．４％とした際にＣ帯の波長域で基本モードであるＬＰ０１モードと第一高次モードであるＬＰ１１モードが伝搬する構造である。 A region indicated by diagonal lines is a region where the LP11 mode satisfies a desired bending loss and does not propagate the LP21 mode. Here, the relative refractive index Δ is expressed by the following equation.

n _core and n _clad are the refractive indices of the core and the cladding, respectively. When a1 = 7 μm and Δ = 0.4%, the LP01 mode that is the fundamental mode and the LP11 mode that is the first higher-order mode propagate in the wavelength band of the C band.

  FIG. 3 shows an Er addition distribution of the optical fiber having the refractive index distribution of FIG. The optical fiber of the present embodiment is an optical fiber mainly composed of silica glass, and in addition to at least one kind of rare earth element, an element for adjusting one or more kinds of refractive index is co-added to the core. . The rare earth element is, for example, Er. Elements for adjusting the refractive index are, for example, aluminum and germanium. In the present embodiment, Er is used as the rare earth element, and Al is used as the element for adjusting the refractive index. Al is added so that the refractive index is 0.4%.

  In the present embodiment, the core has a first region with an Er addition concentration d1 and a second region with an addition concentration d2 higher than d1 in an annular shape. The first region is disposed within a radius a3 from the center of the core. The second region is arranged in a range from the radius a3 to the radius a2 of the cores of the cores. The radius of the core is a1. In the second region, the outer ring radius of the annular part is a2, and the inner ring radius of the annular part is a3.

  FIG. 4 shows that the LP11 mode gain relative to the LP01 mode gain when a3 / a1 is changed from 0 to 1 and d1 / d2 is changed from 0.1 to 1 at a1 = 7 μm, a1 = a2, and d1 = 50 ppm. The gain ratio (dB) is shown. Similarly, FIGS. 5 and 6 show gain ratios when a1 = 4 μm and a1 = 6 μm.

  According to these results, when a3 / a1 is 0.5 or more and less than 0.6, the region where d1 / d2 is 0 or more and 0.375 or less, and when a3 / a1 is 0.6 or more and less than 0.8, When d1 / d2 is 0 or more and 0.44 or less, when a3 / a1 is 0.8 or more and less than 0.9, d1 / d2 is 0 or more and 0.375 or less, and a3 / a1 is 0.9 or more and 1 When the ratio is less than 0, it is understood that the ratio (dB) of the gain of the LP11 mode to the gain of the LP01 mode is 0 dB or more in a region where d1 / d2 is 0 or more and 0.16 or less.

  Next, the gain ratio when a1 <a2 is considered. 7, 8, 9, 10, and 11, a2 / a1 and (a2-a3) when d1 / d2 = 1/10, 1/8, 1/6, 1/4, and 1/2, respectively. The gain ratio between the LP11 mode and the LP01 mode when / a1 is a variable is shown. The core radius at this time is a1 = 4 μm, which is a narrow region having a gain ratio of 0 dB or more.

  As d1 / d2 increases, the region that satisfies the gain ratio of 0 dB or more is small. As shown in FIG. 11, there is no region that satisfies d1 / d2 = 1/2 and the gain ratio of 0 dB or more. I understand.

As shown in FIG. 7, when 0 ≦ d1 / d2 ≦ 1/10,
When a2 / a1 is 0.65 or more and less than 0.7 (a2-a3) / a1 is 0.25 or more and 0.48 or less, or
When a2 / a1 is 0.7 or more and less than 0.8 (a2-a3) / a1 is 0.14 or more and 0.48 or less, or
When a2 / a1 is 0.8 or more and less than 0.9 (a2-a3) / a1 is 0.23 or more and 0.48 or less, or
When a2 / a1 is 0.9 or more and less than 1 (a2-a3) / a1 is 0 or more and 0.48 or less,
It can be seen that the gain ratio between the LP11 mode and the LP01 mode is 0 dB or more.

As shown in FIG. 8, when 1/10 <d1 / d2 ≦ 1/8,
When a2 / a1 is 0.6 or more and less than 0.7 (a2-a3) / a1 is 0.36 or more and 0.47 or less, or
When a2 / a1 is 0.7 or more and less than 0.8 (a2-a3) / a1 is 0.15 or more and 0.49 or less, or
When a2 / a1 is 0.8 or more and less than 0.9 (a2-a3) / a1 is 0.06 or more and 0.49 or less, or
When a2 / a1 is 0.9 or more and less than 1 (a2-a3) / a1 is 0.01 or more and 0.49 or less,
It can be seen that the gain ratio between the LP11 mode and the LP01 mode is 0 dB or more.

As shown in FIG. 9, when 1/8 <d1 / d2 ≦ 1/6,
When a2 / a1 is 0.65 or more and less than 0.7 (a2-a3) / a1 is 0.3 or more and 0.47 or less, or
When a2 / a1 is 0.7 or more and less than 0.8 (a2-a3) / a1 is 0.24 or more and 0.47 or less, or
When a2 / a1 is 0.8 or more and less than 1 (a2-a3) / a1 is 0.17 or more and 0.47 or less,
It can be seen that the gain ratio between the LP11 mode and the LP01 mode is 0 dB or more.

As shown in FIG. 10, when 1/6 <d1 / d2 ≦ 1/4,
When a2 / a1 is 0.7 or more and less than 0.8 (a2-a3) / a1 is 0.36 or more and 0.43 or less, or
When a2 / a1 is 0.8 or more and less than 0.9 (a2-a3) / a1 is 0.27 or more and 0.43 or less, or
When a2 / a1 is 0.9 or more and less than 1 (a2-a3) / a1 is 0.35 or more and 0.43 or less,
It can be seen that the gain ratio between the LP11 mode and the LP01 mode is 0 dB or more.

The amplification optical fiber of the present invention can be applied to the information and communication industry because it realizes a long distance in transmission using a plurality of modes.

Claims (7)

An optical fiber mainly composed of silica glass having a core and a clad having a refractive index lower than that of the core around the core and having a step-type refractive index profile formed therein.
A first region of the core disposed within a radius a3 from the center of the core and having a rare earth element concentration d1;
A second region of the core that is disposed in a range of a radius a3 to a radius a2 of the core and that has a rare earth element concentration d2.
a2 = a1, 0.5 ≦ a3 / a1 <0.6, d1 / d2 ≦ 0.375, or
a2 = a1, 0.6 ≦ a3 / a1 <0.8, d1 / d2 ≦ 0.44, or
a2 = a1, 0.8 ≦ a3 / a1 <0.9, and d1 / d2 ≦ 0.375, or
An optical fiber, wherein a2 = a1, 0.9 ≦ a3 / a1 <1, and d1 / d2 ≦ 0.16. An optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile,
A first region of the core disposed within a radius a3 from the center of the core and having a rare earth element concentration d1;
A second region of the core that is disposed in a range of a radius a3 to a radius a2 of the core and that has a rare earth element concentration d2.
0 ≦ d1 / d2 ≦ 1/10, 0.65 ≦ a2 / a1 <0.7, and 0.25 ≦ (a2−a3) /a1≦0.48, or
0 ≦ d1 / d2 ≦ 1/10, 0.7 ≦ a2 / a1 <0.8, 0.14 ≦ (a2−a3) /a1≦0.48, or
0 ≦ d1 / d2 ≦ 1/10, 0.8 ≦ a2 / a1 <0.9, and 0.023 ≦ (a2-a3) /a1≦0.48, or
0 ≦ d1 / d2 ≦ 1/10, 0.9 ≦ a2 / a1 <1.0, and 0.0 ≦ (a2-a3) /a1≦0.48 . An optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile,
A first region of the core disposed within a radius a3 from the center of the core and having a rare earth element concentration d1;
A second region of the core that is disposed in a range of a radius a3 to a radius a2 of the core and that has a rare earth element concentration d2.
1/10 <d1 / d2 ≦ 1/8, 0.6 ≦ a2 / a1 <0.7, and 0.36 ≦ (a2−a3) /a1≦0.47, or
1/10 <d1 / d2 ≦ 1/8, 0.7 ≦ a2 / a1 <0.8 and 0.15 ≦ (a2−a3) /a1≦0.49, or
1/10 <d1 / d2 ≦ 1/8, 0.8 ≦ a2 / a1 <0.9, and 0.06 ≦ (a2−a3) /a1≦0.49, or
1/10 <d1 / d2 ≦ 1/8, 0.9 ≦ a2 / a1 <1.0, and 0.01 ≦ (a2−a3) /a1≦0.49 Optical fiber. An optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile,
A first region of the core disposed within a radius a3 from the center of the core and having a rare earth element concentration d1;
A second region of the core that is disposed in a range of a radius a3 to a radius a2 of the core and that has a rare earth element concentration d2.
1/8 <d1 / d2 ≦ 1/6, 0.65 ≦ a2 / a1 <0.7, and 0.3 ≦ (a2−a3) /a1≦0.47, or
1/8 <d1 / d2 ≦ 1/6, 0.7 ≦ a2 / a1 <0.8, and 0.24 ≦ (a2−a3) /a1≦0.47, or
1/8 <d1 / d2 ≦ 1/6, 0.8 ≦ a2 / a1 <1.0, and 0.17 ≦ (a2−a3) /a1≦0.47 Optical fiber. An optical fiber mainly composed of silica glass having a core and a clad and having a step-type refractive index profile,
A first region of the core disposed within a radius a3 from the center of the core and having a rare earth element concentration d1;
A second region of the core that is disposed in a range of a radius a3 to a radius a2 of the core and that has a rare earth element concentration d2.
1/6 <d1 / d2 ≦ 1/4, 0.7 ≦ a2 / a1 <0.8, and 0.36 ≦ (a2−a3) /a1≦0.43, or
1/6 <d1 / d2 ≦ 1/4, 0.8 ≦ a2 / a1 <0.9, and 0.27 ≦ (a2−a3) /a1≦0.43, or
1/6 <d1 / d2 ≦ 1/4, 0.9 ≦ a2 / a1 <1.0, and 0.35 ≦ (a2−a3) /a1≦0.43 Optical fiber.   The optical fiber according to claim 1, wherein the rare earth element contains erbium.   The optical fiber according to claim 1, wherein aluminum or germanium is added to the core in addition to the rare earth element.

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